1. Field of the Invention
The present invention relates generally to steam turbine rotor blades and, more specifically, to a freestanding blade design for a row of rotating blades mounted on a turbine rotor, in which alternating blades have differently tuned natural frequencies.
2. Description of the Related Art
Steam turbine rotor blades are arranged in a plurality of rows or stages. The rotor blades of a given row are normally identical to each other and mounted in a mounting groove provided in the turbine rotor.
Turbine rotor blades typically share the same basic shape. Each has a root receivable in the mounting groove of the rotor, a platform which overlies the outer surface of the rotor at the upper terminus of the root, and an airfoil which extends upwardly from the platform.
The airfoils of most steam turbine rotor blades include a leading edge, a trailing edge, a concave surface, a convex surface, and a tip at the distal end opposite the root. The airfoil shape common to a particular row of rotor blades differs from the airfoil shape for every other row within a particular turbine. Likewise, no two turbines of different designs share airfoils of the same shape. The structural differences in airfoil shape result in significant variations in aerodynamic characteristics, stress patterns, operating temperature, and natural frequency of the airfoil. These variations, in turn, determine the operating life of the rotor blades within the boundary conditions (turbine inlet temperature, pressure ratio, and engine speed), which are generally determined prior to the airfoil shape development.
Development of a turbine section for a new commercial, power generation stream turbine may require several years to complete. When designing rotor blades for a new steam turbine, a profile developer is given a certain flow field with which to work. The flow field is determined by the inlet and outlet angles (for steam passing between adjacent rotor blades of a row), gauging, and the velocity ratio, among other things. "Gauging" is the ratio of throat to pitch; "throat" is the straight line distance between the trailing edge of one rotor blade and the vacuum side surface of an adjacent blade, and "pitch" is the distance between the trailing edges of the adjacent rotor blades.
These flow field parameters are dependent on a number of factors, including the length of the rotor blades of a particular row. The length of the blades is established early in the design stages of the steam turbine and is essentially a function of the overall designed power output of the steam turbine and the power output for that particular stage.
Blades of a given row may be "freestanding", meaning that individual blades of a row are not connected to each other, they may be lashed or shrouded together in groups.
An essential aspect of the rotor blade design is the "tuning" of the natural frequency of the rotor blade so as to avoid natural frequencies which coincide with or approximate the harmonics of running speed. Such coincidence causes the blades to vibrate in resonance, thereby leading to blade failure. Therefore, in the process of designing and fabricating turbine rotor blades, it is critically important to tune the resonant frequencies of the blades to minimize forced or resonant vibration.
To do this, the blades must be tuned to avoid the "harmonics of running speed". The harmonics of running speed is best explained by example. In a typical fossil fuel powered steam turbine, the rotor rotates at 3,600 revolutions per minute (rpm), or 60 "cycles" per second (cps). Since one cps equals 1 hertz (Hz), and since simple harmonic motion can be described in terms of the angular frequency of circular motion, the running speed of 60 cps produces a first harmonic of 60 Hz, a second harmonic of 120 Hz, a third harmonic of 180 Hz, a fourth harmonic of 240 Hz, etc. The harmonic series of frequencies, occurring at intervals of 60 Hz, represent the characteristic frequencies of the normal modes of vibration of an exciting force acting upon the rotor blades. If the natural frequencies of oscillation of the rotor blades coincide with the frequencies of the harmonic series, or harmonics of running speed, a destructive resonance can result at one or more of the harmonic frequencies.
Given that exciting forces can occur at a series of frequencies, a blade designer must ensure that the natural resonant frequencies of the blades do not fall on or near any of the frequencies of the harmonic series. This would be an easier task if rotor blades are susceptible to vibration in only one direction. However, a rotor blade is susceptible to vibration in potentially an infinite number of directions. Each direction of vibration will have a different corresponding natural frequency. The multi-directional nature of blade vibration is referred to as the "modes of vibration". Each mode of vibration establishes a different natural resonant frequency for a given rotor blade for a given direction.
Keeping in mind the harmonic series described above for a fossil fuel powered steam turbine operating at 3,600 rpm the natural resonant frequency for a rotor blade must be tuned to avoid frequencies at intervals of 60 Hz. For example, the second harmonic occurs at 120 Hz and the third harmonic occurs at 180 Hz. The standard practice is to attempt to tune the blade having a frequency falling somewhere between 120-180 Hz to come as close as possible to the mid point between the two harmonics, i.e., 150 Hz. If a rotor blade has a natural resonant frequency which falls between the second and third harmonics for the first mode of vibration, it would be desirable to tune the blade to have a frequency at or near 150 Hz for the first mode of vibration.
Frequencies for other modes of vibration are similarly tuned to be as close as possible to a midpoint between two successive harmonics. However, frequency tests are commonly run up to and beyond a seventh mode of vibration; a frequency near the seventh harmonic (420 Hz) might be expected.
When a new steam turbine is designed, the blade designer must tune the turbine blades so that none of the resonant frequencies for any of the modes of vibration coincide with the frequencies associated with the harmonics of running speed. Sometimes, tuning requires a trade off with turbine performance or efficiency. For instance, certain design changes may have to be made to the blade to achieve a desired natural frequency in a particular mode. This may necessitate an undesirable change elsewhere in the turbine such as a change in the velocity ratio or a change in the pitch and Width of the blade root.
As previously mentioned, the rotor blades of a given row are identical. But, to avoid certain aerodynamic problems, such as aeroelastic instability, where two adjacent blades having the same natural frequencies can excite each other, a method of mix-tuning is used. This method provides that two adjacent blades will have differing natural frequencies thus preventing aeroelastic instability. This method is achieved using two different profile tip lengths on adjacent blades in a row.
Westinghouse Electric Corporation, the Assignee of the present application, makes numerous different steam turbines which can be identified by their building block (BB) numbers. A BB70, for example, will have individual rows of stationary and rotating blades identified by their respective positions vis-a-vis the steam inlet. The L-2R row is the second row of rotating blades from the steam exit. Blade length progressively increases as distance from the inlet increases. The BB70 L-2R row has 136 blades per row, while the BB71 has 154 blades per row.
Side entry root/group configurations are commonly used to attach the blade of a given row to the rotor. Straight side entry root/groove configurations are characterized by a linear root center line, while curved side entry configurations have arcuate root center lines. Depending on the type of root, special mounting problems arise, particularly when installing the last blade of a row.
The blade currently used in the L-2R row of the BB70 and BB71 turbines has shrouded tips and is mounted on a straight side entry root/groove configuration. The blades are locked together at the shrouds, and thus a platform-to-platform locking pin is not required.
If it becomes necessary to retrofit an existing turbine with freestanding blades, or to replace original designed shrouded blades with freestanding blades, a problem arises with respect to mounting and locking together the last blade of a row. Platform-to-platform pinning, as described in U.S. Pat. No. 4,767,275 issued to Brown, is suitable for curved side entry blades, but has not heretofore been used for freestanding straight side entry blades.